Practice Solving Differential Equations Using Fourier Transform - 11.9 | 11. Fourier Transform and Properties | Mathematics (Civil Engineering -1)
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

11.9 - Solving Differential Equations Using Fourier Transform

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the Fourier Transform used for in solving ODEs?

💡 Hint: Consider how transforms change the perspective on the equations.

Question 2

Easy

Name the main benefit of using the Fourier Transform for differential equations.

💡 Hint: Think about the complexity of dealing with derivatives.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the primary advantage of using Fourier Transform to solve ODEs?

  • It eliminates the need for initial conditions.
  • It converts differential equations into algebraic equations.
  • It simplifies the equations with non-linear terms.

💡 Hint: Think about how complex the derivatives make the equation before transformation.

Question 2

True or False: The Inverse Fourier Transform is used to convert frequency domain data back to the time domain.

  • True
  • False

💡 Hint: Recall the purpose of the Inverse Transform.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Solve the differential equation d²y/dt² - 4y = sin(t) using the Fourier Transform method.

💡 Hint: Pay attention to how sine functions convert in the frequency domain.

Question 2

Consider the ODE d²y/dt² + 5dy/dt + 6y = e^(-t) for t > 0. Use Fourier Transform methods to find y(t) for t > 0.

💡 Hint: Remember to handle the exponential function carefully when transforming.

Challenge and get performance evaluation